Such an electrical impedance tomography device (EIT device) is known, for example, from EP 1 000 580 A1, which is used to record an “electrical impedance tomography image” of a cross section of the body of a patient.
Electrical impedance tomography is a process for reconstructing impedance distributions or impedance changes relative to a reference distribution in electrically conductive bodies. A plurality of electrodes are applied for this to the conductive surface of the body being examined, and the control unit, usually a digital signal processor, ensures that a pair each of (preferably) adjacent electrodes is supplied consecutively with an electric alternating voltage (for example, 5 mA at 50 kHz) and the electric voltages are detected at the remaining electrodes and sent to the control unit. Due to the combination of the measured voltage values during the consecutive rotating current feeds, the impedance distribution or the change thereof relative to a reference distribution can be reconstructed with suitable algorithms. A ring-shaped, equidistant arrangement of 16 electrodes, which can be placed, for example, around the body of a patient with a belt, is used in typical applications. Alternating current is fed into two adjacent electrodes each and the voltages are measured between the remaining currentless electrode pairs and received by the control unit. A plurality of measured voltage values, from which a two-dimensional tomogram of the impedance distribution relative to a reference in the electrode plane can be reconstructed, are obtained by rotating the current feed points.
Electrical impedance tomography has been increasingly used in medical research. Typical EIT devices use 8, 16 or 32 electrodes for data acquisition, with current (voltage) being fed (applied) to two or more electrodes and the resulting voltage (current) being measured between the remaining electrodes. The first variant shall be considered below. The second variant may be considered analogously by replacing current and voltage as the feed and measured variable. By combining different feeds and measurements, it is possible to generate a signal vector, from which the impedance distribution can be determined by means of a suitable algorithm or the relative change in the impedance distribution relative to a reference value can be determined in the electrode plane in case of a functional EIT (fEIT). The latter is used for the state-dependent fEIT of the thorax, in which N electrodes are arranged in a ring-shaped pattern around the thorax in order to reconstruct from the comparison of the signal vectors in different states of the lungs (e.g., end-inspiratory and end-expiratory states) a tomogram of the ventilation-related relative impedance change, which is an indicator of the regional distribution of the ventilation of the lungs. The components of the signal vector, i.e., the voltages here, are assigned an unambiguous combination of current feed electrode pair and voltage-measuring electrode pair. This combination is called a channel or measuring channel here. The so-called adjacent data acquisition, where current is fed between two adjacent electrodes and the voltages are measured between the remaining adjacent electrode pairs, is frequently used. A total of 16*13=208 measuring channels, see FIG. 1, are obtained here from 16 current feeds and 13 measuring pairs. Based on the reciprocity when transposing current feed and voltage measurement, only 104 of them are linearly independent. The measured voltage value vector, from which a tomogram can be calculated (frame), is formed from the voltage measurements of the channels. The adjacent DAQ mode is characterized by high sensitivity with respect to relative impedance changes, but it has the drawback that very low voltages appear at times, which may contain an error. Greater distances between current feed and/or voltage measurement are more robust in this respect, but sensitivity is, in general, lost.
From a mathematical physical point of view, EIT is an ill-posed, inverse, nonlinear problem. This means that small errors in the measured boundary voltages are manifested in very great errors in the inverse solution, conductivity distribution or impedance distribution and the solution does not in general, always depend on measured erroneous marginal voltages. The ill-posedness persists even in the linearized case of functional thoracic EIT with small changes in the state of the lungs due to ventilation relative to a reference state of the lungs. In case of matrix representation of the reconstruction, this is reflected, in general, by a poor condition of matrices, which describe the relationship between changes in conductivity (or impedance changes) in the interior of the object studied and changes of the measured voltages at the edge of the object studied with known current feed. Mathematical methods, e.g., regularization for cushioning the poor conditions, are therefore used, but this leads to a limitation of the solution space and a reduction of spatial resolution.
A middle-of-the-road approach is typically sought between robustness to measuring errors and resolution. The regularization strength is controlled based on a so-called regularization parameter, which is adapted to the signal-to-noise ratio (SNR) found. Measured values with different noises in the reconstruction process may possibly also be weighted differently with the correlation matrix analogously to a weighted mean valuex=(Σxi/σi2)/(Σ1/σi2)with σi as the statistical error of a measured variable xi. The SNR is primarily a device-specific variable, for which the hardware of many EIT systems is optimized. A fixed reconstruction rule, once generated, which takes into account the SNR, e.g., in weighting and/or regularization, is therefore usually used as a reconstruction. This usually suffices for laboratory experiments with fairly constant and idealized environment.
However, the concept of a fixed reconstruction rule often proves to be insufficient in the daily practice of clinical application. It is seen, in particular, that simply taking statistical errors (SNR) into account alone for the reconstruction rule is often not robust enough for the practical clinical application of EIT. With modern electronics and computer technology, noise does not usually prove to be a limiting factor of a successful measurement. The measuring errors, which form marked artifacts in electric impedance tomograms, are mostly of a systematic nature. These systematic measuring errors are caused, e.g., by common mode voltages or inductive crosstalk (capacitive crosstalk can often be properly screened). In addition, these measuring errors often change over time. This exact value of the systematic measuring errors is typically unknown, so that correction of the voltages themselves is usually impossible. Current EIT systems were used to a great deal under laboratory conditions with phantoms or on healthy volunteers, where the relative systematic error component is very small. Therefore, these interferences are not taken into account by the current reconstruction rules in EIT. However, it is often seen in routine clinical practice in patients with critical lung diseases that the relative systematic error component of the measured voltages may be very large. Ignorance of these errors may then lead to enormous artifacts in reconstructed EIT images, which makes medical interpretation impossible.
The adaptation of the reconstruction is usually applied when measurements containing great errors occur in applications in which these are expected. If, for example, a mean value of 100 measurements shall be formed and measurement 33 is known to have been a “measuring error,” this is discarded and the mean value is formed from the remaining 99 measurements. However, no such adaptation of the reconstruction rule has hitherto been performed in EIT. A full data set of all measuring channels is assumed in all reconstructions published so far, and the SNR is taken into account at best by weighting on the basis of the statistical measuring error via the correlation matrix, and systematic measuring errors are ignored by the current reconstruction rules in EIT.